The Penrose Transform and the Kerr-Schild double copy

There are a number of classical double copies, each providing a prescription for generating solutions to the Maxwell and scalar wave equations from exact solutions of Einstein's equations. Two such prescriptions are the Kerr-Schild and twistorial double copies. We argue that for a broad class of self-dual vacuum solutions of the Kerr-Schild form, which we refer to as twistorial Kerr-Schild spacetimes, these two prescriptions are in fact equivalent. The approach is elementary, utilizing null Lorentz transformations, with homogenous functions on twistor space playing a central role. The equivalence is illustrated explicitly for the example of the self-dual (Kerr)-Taub-NUT spacetime. A detailed proof and several more examples will be presented in a long-form companion to this letter.